Topic 5 page 1

Topic 5: Monopoly

Price and Output Decisions Under Monopoly Assumptions of a Pure Monopolist: 1) C__________ cannot enter the industry 2) No close ___________. In order to maximize profit, an unregulated monopolist will choose the price and output levels at which the difference between total revenue and total cost is largest.

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Output Price TR TC Total Profit

2 400 800 640 3 350 1,050 790 4 342.5 1,370 960 5 331 1,655 1,150 6 311 1,866 1,361 7 278 1,946 1,590 8 250 2,000 1,840

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Revenue, Cost, Profit TR 2000 TC 1600 Max Profit 1200 800 400 0 2 4 6 8 10 Output

Under monopoly the firm will maximize profit if it sets its output rate at the point at which marginal ____ equals marginal _______.

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Output MC MR Total Profit

3 150 250 4 170 320 5 190 285 6 211 * 211 * 7 229 80 8 250 54

(MC and MR figures pertain to the interval between the indicated quantity of output and one unit less than the indicated quantity of output.)

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Dollar per Unit of Output 320 280 MC 240 200 160 120 80 40 MR 0 0 2 4 6 8 output The point where MC = MR is a necessary condition for ____ maximization.

At profit maximizing output (5 or 6) MC=MR.

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Proof: Let Π represent the firm’s profit. Then, the monopolist’s profit equals: π = −TR TC and the change in profit due to a change in output is:

∂π∂

∂∂

∂∂Q

TRQ

TCQ

= −

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Setting ∂π∂Q

= 0 to obtain the conditions under which profit is at a maximum, we find that:

∂∂

∂∂

TRQ

TCQ

MR MC

=

=

Thus, marginal revenue must equal marginal ____ when profits are maximized. (Slope of the profit function is ____ when profit is maximized)

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The Output and Price Decision The price and output decision of the monopolist are shown in the figure: Price MC 10 A AC 6 C 5 B MC=MR Demand MR 100 Output

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Profit=10-A-C-6=(4)*(100)=______ To maximize profit, the monopolist should produce an output where ___curve intersects the __ curve. If the monopolist produced Q=100 units, the demand curve shows that it must set a price of P=$10.

Note: Since the monopolist is the only member of the industry, the demand curve for the output of the monopolist is the industry demand curve. So, in contrast to perfect competition, where the demand curve of the individual firm is horizontal, the demand curve for the monopolists’ output, slopes downward and to the right.

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Most monopolized industries set a higher ____ and produce a lower output than in a perfectly competitive market. This is because the perfectly competitive firm operates at the point where _____ equals MC, whereas the monopolist operates at a point at which _____ is greater than MC. To see this consider the following proof:

MR PPE

= −⎛⎝⎜

⎞⎠⎟1

1

where MR is the marginal revenue P is the price PE is the price elasticity of demand

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Since monopolists set marginal revenue equal to marginal cost, it follows that at the point where profit is maximized:

MR MC PPE

= = −⎛⎝⎜

⎞⎠⎟1

1

Re-arranging the above expression:

P

MC

PE

=−

⎛⎝⎜

⎞⎠⎟1

1

And, since |PE|>0, it follows that 11

1−⎛⎝⎜

⎞⎠⎟ <

PEand p____ must be

greater than MC.

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Numerical Illustration: The Kentwood Company: To illustrate how price and output can be chosen to maximize profit, consider the Kentwood Company, a monopolist, producing and selling a product with the demand curve:

P= 30 - 6Q

where P is price in ($’ thousands), and Q is the firm’s output ( in thousands of units).

The firm’s total cost function is: C = 14 + 3Q + 3Q2 where C is total cost in ($’s million).

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From the demand curve, we can determine the firm’s total revenue which is: TR = PQ = (30 - 6Q) Q= 30Q - 6Q2

Thus, marginal revenue equals:

∂∂

∂∂

TRQ

Q QQ

Q=−

= −( )30 6

30 122

From the total cost function, we can determine the marginal cost:

MC = =+ +

= +∂∂

∂∂

TCQ

Q QQ

Q( )14 3 3

3 62

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Setting MR=MC:

30 12Q 3 6Q− = + and solving for Q, we find that Q=1.5.

Inserting 1.5 for Q in the demand curve equation, P=30-6Q, we find that P= 21. Thus, to maximize profit, the Kentwood Company should set a price of $21,000 and produce and sell 1.5 thousand units.

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If it does, its profit will equal: [30(1.5) - 6(1.5)2] - [14 + 3(1.5) + 3 (1.5)2] = $6.25 million (TR) - (TC) = profit

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Two Part Tariffs A monopolist sometimes requires the consumer to pay an initial ____for the right to buy its product as well as a usage fee for each unit of the product that he or she buys. This is known as a two part tariff. Examples: Telephone companies charge a basic monthly fee for telephone service plus an amount for usage. Hydro: basic minimum plus usage

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If a monopolist uses this pricing technique, it must determine how high the initial fee must be as well as the size of the usage fee. The lower the initial fee, the greater the number of consumers that will purchase the right to buy the product. Hence, lower initial fees are likely to result in greater ______ from the sales of the product. But, low initial fees may eat into the _______ of the firm. Consequently, the monopolist would be expected to choose the initial fee and usage fee so that its total profit is at a maximum.

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Example: Disneyland, in California, used to charge an entrance fee and a fee for each ride the customer went on. In the early 1980s, Disneyland eliminated the fee for individual rides and raised the entrance fee. The managers at Disneyland must have concluded that this would increase the park’s profits.

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The Social Objection to Monopoly

To illustrate, compare the prices and quantities produced under monopoly and perfect competition and determine the social cost of monopoly.

Price Price A A Pm C Dead Weight Loss PC B SL PC B MCL D D D MR 0 Qc Quantity 0 Qm Qc Quantity

Competitive Industry Monopoly

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The first diagram shows the competitive price and output in a competitive industry. ►Consumer surplus is equal to PcAB. In the long run, the supply function is horizontal. ►Producer surplus is zero. In the second diagram the monopoly price is Pm and output is Qm. Price is higher and quantity produced is lower. ►Consumer surplus is smaller and is equal to PmAC.

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A monopoly transfers part of consumer surplus to the monopolist through profits earned by the monopolist: Area PcPmCD. Since output is smaller, the monopoly creates a deadweight loss of monopoly equal to area DCB. The social objection to monopoly is that it creates a deadweight loss, so total _______ is not maximized.

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Note: The primary complaint about monopoly is that the monopolist produces too few ____, not that it charges too high a _____. Since fewer resources are employed in the monopolistic market, resources are inefficiently allocated into other industries.